Wow, that IS tricky, isn't it? My gut feeling would be to tell him before and give him time to get used to the idea. He might be upset if you spring this on him on the day and could cause bad feeling. If he's the sort of person who would make a big fuss about this it might be an idea to remind him that it's his daughter's special day and that he needs to be a grown up about it. After all he doesn't have to have anything to do with the woman, does he? As you're on good terms with her, maybe you could mention to her that you'd appreciate her keeping out of his way (if it's a problem for him).